You know, I’m always surprised by how many fics nail the 'aristocratic rebel' angle better than some canon-compliant stuff. There's this tension between the Black family legacy he's running from and the person he's trying to become at Hogwarts that gets explored in a million ways. Some writers really lean into the idea that his loud, reckless persona is a performance, a shield against the expectations he was raised with. You'll find fics where he's hyper-competent at pure-blood politics but uses it to sabotage his own family, or ones where the bravado cracks during the full moon when it's just him and Remus.
What I find more interesting, though, are the stories that tie his development to his relationship with space—both metaphorical and literal. Grimmauld Place is a prison, but so is his own name, his face that looks so much like his family's. A lot of authors have him constantly moving, running, flying, never stopping, because stopping means confronting what he's carrying. That restlessness defines him, and his character arc in fanfiction often becomes about learning when to stay, or who to stay for. Sometimes it's James, sometimes Remus, sometimes even Regulus. The best fics don't just make him 'the cool godfather'; they show the cost of building a new identity from scratch while haunted by the old one.